Question

A box contains three marbles, one red, one blue, and one green. Describe the sample space of each of the following experiments:

(a) First draw a marble from the box, record its color, replace the marble in the box, and draw a marble again.

(b) Draw two marbles without replacing the first one.

Answer 1

this event consists of a drawing of a total number of 2 balls from the box
since the ball is replaced after taking, we can take any of the 3balls during the second attempt and the sample space will be:

[ (red,red) (red,blue) (red,green) (blue,red) (blue,blue)(blue,green) (green,red) (green,blue) (green,green)]

the first color indicates the ball taken during the first attempt, and 2nd color indicated the ball taken after replacing the ball in the box.

now if the ball is not replaced in the box after taking it, only two balls will be left if we take 1 ball, hence only 2 possibilities will be there in the 2nd attempt
so, the sample space will be:

[ (red,blue) (red,green) (blue,red) (blue,green) (green,red) (green,blue)]